We developed a mathematical model of the melting zone of a single-screw extruder for processing of polymers. The model takes into account a heat transfer of a polymer with a worm and a cylinder of an extruder (parameters of a heat transfer agent in the worm, as well as parameters of a heat carrier or electric heaters on the outer surface of the cylinder), as well as the real boundary conditions (the worm rotates, the cylinder is fixed).The classical and most commonly spread plane-parallel model of the melting process, in contrast to the developed model, considers a fixed worm and a rotating cylinder extended on the plane. Therefore, processes that actually occur near the surface of a rotating worm are conditionally transferred to the side of a fixed cylinder and vice versa. It distorts fields of speed and temperature of a polymer in the worm channel, as well as the viscosity value of a polymer along the channel height.We investigated a temperature field of a polymer in the worm channel, as well as a relative width of a polymeric stopper along the length of the melting zone of the extruder (the ratio of a width of the polymer stopper to a width of the worm channel). We compared results of the calculation with the experiment. We showed that the proposed model describes the process of melting of a polymer better than the classical inverse plane-parallel model. We also proposed the approach to modeling of an extruder in general as sequences of its interconnected functional zones.The difference between calculated and measured values of the dimensionless width of the polymeric "stopper" from the dimensionless coordinate along the axis of the worm does not exceed 15 %. This is less than at using the traditional approach to modeling of the melting process.The developed technique was successfully implemented for the modes of processing of various polymeric materials at extruders with worms of diameter 32, 45, 63, 90, and 125 mm.The use of the developed mathematical model will make it possible to better forecast effective modes of the worm extruder, especially if it is necessary to account for heat transfer between surfaces of a worm and a cylinder, as well as processing of materials characterized by low thermal resistance